Chemistry

Question

The atomic radius of metal X is 125 picometers (pm) and a crystal of metal X has a unit cell that is face-centered cubic. Calculate the density of metal X (atomic weight = 42.3 g/mol).

1 Answer

  • We have that the Density of metal X  is mathematically given as

    [tex]\phi= 6359.44 Kg/m^3[/tex]

    Density of metal

    Generally the equation for the side of fcc  is mathematically given as

    [tex]Fcc=2*\sqrt(2) *radius of metal\\\\Fcc== 2*1.414*125\\\\Fcc 353.5*10^-12 m \\\\[/tex]

    Where

    volume of 1 unit cell of fcc

    [tex]FccV= (353.5*10^-12)^3\\\\FccV =44174155.375 *10^-36 m^3\\\\[/tex]

    And

    weight of 1 atom

    [tex]Wa= moleular weight / avogadro number\\\\Wa = 42.3/(6.023 *10^23) \\\\Wa= 7.023 *10^-23 gm/atom\\\\[/tex]

    Therefore

    density

    [tex]\phi= (28.0923 *10^-26) / ( 44174155.375 *10^-36)[/tex]

    [tex]\phi= 6359.44 Kg/m^3[/tex]

    For more information on Atoms visit

    https://brainly.com/question/13981855

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